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What are mechanical resonance and damping in engineering?

In our previous articles, such as our article on axial load-carrying capacity, we focused on buckling and load-carrying calculations.  In our next few articles, we’ll move on to focusing on the vibration of structures and how it can affect them.

What is vibration in engineering?

Let’s dive into some of the concepts of vibration so that we can understand resonance and damping.  All structures are flexible to some extent, and vibration is the consequence of a structure due to its flexible nature.  This results in an oscillatory motion. 

Vibrations may be totally unnoticeable to humans using a structure or machine.  On the other hand, it can become a health problem due to excessive vibration, for example, with a power tool.  With these types of issues, occupational diseases such as vibrational white finger are common.

The vibration can even affect the structural integrity of a structure and result in its failure.  An example of this is the famous Tacoma Narrows Bridge.

What is resonance?

Now that we know what vibration is, let’s look at resonance.  Resonance affects all structures, and it’s possible to affect a structure, such as breaking a wine glass, by exciting it at the same frequency as its resonance frequency.

All structures have a ‘natural frequency’. It’s the frequency at which the structure vibrates with a very high amplitude if excited at that same frequency. For the purposes of this article, we are interested in those frequencies that are in the range at which we would typically excite the structure.

For example, say we take a typical motor car with an internal combustion engine operating within the engine speed range of 1000–6000 RPM. This corresponds to an excitation frequency range of:

f1 = 1000 / 60 = 16.6 Hz

f2 = 6000 / 60 = 100Hz

If the vehicle has a 4-stroke cycle with 4 cylinders, then this equates to 2 firing events per cycle of the engine crank. In other words, the engine will excite the structure of the car chassis and body with a frequency in the range of 33.2 Hz (2 x 16.6 Hz) to 200 Hz (2 x 100 Hz). If we ignore harmonics, then it is reasonable to conclude that the vehicle is not going to be excited at any of the resonant frequencies that exist above 200 Hz. 

What is damping?

We can conclude that there are natural frequencies inherent in structures.  These frequencies, if excited, will cause an uncontrolled amplitude response, which could potentially have catastrophic consequences.

The energy of these large amplitude responses at resonance can be counteracted by the inclusion of damping. Damping is any mechanism that serves to absorb the energy of resonance and hence reduce the amplitude of response. The energy of the high amplitude response is converted to heat.

Think about the typical motor vehicle from our example above, which will have a damping element attached to each suspension system. At a simple level, this consists of a cylinder containing oil, and this is known as fluid viscous damping. These types of dampers are also commonly used in tall skyscrapers to minimise vibration response to earthquakes and wind loads.

In other words, damping is introduced into a structure to reduce the amplitude of the response.

We’re going to continue our series with more interesting facts on vibration and how it affects civil engineering structures.

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